Let's sale the name Big Twelve to the Big Ten for a trillion dollars.
I actually don't think we even own the trademark on "Big Twelve"
According to official documentation, the name of the conference is "Big 12 Conference" and I'm pretty sure the trademark is "Big 12"
So if they wanted to call it the "Big XII" or "Big Twelve", I don't think they'd be violating any trademarks.
I thought I heard once that the Big12 actually owned rights to every reasonable number except 10--including 11 and 16.